We compute the shortest sequence of local connectivity modifications that transform a genus 0 quad mesh to a polycube. The modification operations are (dual) loop preserving and thus, we are restricted to quad meshes where loops don't self-intersect and two loops intersect at most twice. The intersection patterns of the loops are encoded in a simplicial complex, which we call loop complex. To formulate the modification search over the loop complex, we characterise polycubes combinatorially and determine dependencies between modifications. We show that the full task can be encoded as a mixed-integer problem that is solved by a commodity MIP-solver. We demonstrate the practical feasibility by a number of examples with varying complexity.

我们计算将亏格 0 四边形网格转换为多立方体的最短局部连通性修改序列。修改操作是（双）循环保留，因此，我们仅限于循环不自相交且两个循环最多相交两次的四边形网格。循环的交集模式被编码在一个单纯复形中，我们称之为循环复形。为了在循环复合体上制定修改搜索，我们以组合方式表征多立方体并确定修改之间的依赖关系。我们表明，完整的任务可以编码为一个混合整数问题，由商品 MIP 求解器解决。我们通过许多具有不同复杂性的示例来证明实际可行性。